New methods have been developed for measurement of homo- and heteronuclear J couplings in isotopically enriched proteins. These methods permit these J couplings to be measured at an unusually high precision of ca 0.1 Hz. Nearly forty years ago, Karplus demonstrated an empirical relation between the size of the three-bond J coupling and the intervening dihedral angle. Besides the dihedral angle, J couplings are also known to be influenced by a number of other factors, such as substituent effects, electric field gradients, and bond strain. In proteins, there are four three-bond J couplings that describe the backbone angle phi. All four J couplings have been measured for most of the amino acid residues in a small model protein, ubiquitin. Comparison of the measured J couplings with the phi angles calculated from the X-ray structure of this protein allowed reparametrization of the "Karplus relationships" which previously had been based on the measurement of J couplings in constrained small model compounds. Although qualitatively similar, the new parametrizations deviate considerably from the commonly used literature values. Concerted use of all four J couplings for a given residue allows the 4) angle to be determined at high precision. Results indicate that the uncertainty in the NMR-derived phi angle is ca 2 degrees, which compares favorably with the uncertainty of ca 3.2 degrees observed for the phi angle in the X-ray structure of basic pancreatic trypsin inhibitor, solved at 1-Angstroms resolution.